The measure would give workers at businesses with 10 employees or more nine paid sick days per year, while those at smaller companies would get five days. Businesses would be fined $1,000 per violation.

The measure is championed by a coalition of labor and community groups and has been hailed by health experts as a way to contend with the H1N1 virus. About 1 million New York workers have no paid sick days, according to a study by the Community Service Society of New York. A separate study by Restaurant Opportunities Centers United shows that 84 percent of restaurant workers don’t get paid sick days and 52 percent have gone to work when ill.

New York Mayor Michael Bloomberg has expressed support for requiring large companies to provide paid sick days but has stopped short of saying that small businesses should.

Council Speaker Christine Quinn has yet to take a stance. The bill is likely to stir up fears among small-business owners who worry that they could not afford to comply with the mandate, especially during tough economic times.

“The City Council has been trying to ease regulations for small businesses,” said one small-business leader. “And then here you go—what you give with one hand you take with the other.”

But supporters are already close to the 34 council votes they’d need to override a mayoral veto, so they might be able to pass this bill even if small-business owners protest and the mayor heeds their call.